Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator

By Stephen Joe, Frances Y. Kuo. TOMS, 2003

443 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d64193b04a708d93695ee60ba7854a636880a353

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Support points (2016, methodology): “The latter is obtained by (a) generating a randomized Sobol’ sequence using the R package randtoolbox [14] (which employs Owenstyle scrambling [51] with Sobol’ sequences generated in the implementation of [29]), and (b) performing the inverse-transform of F on the resulting point set.”
Multimodality and Global Optimization in Aerodynamic Design (2013, methodology): “The list of numbers md;n used in this work is provided by Joe and Kuo [23] and can be used for dimensions up to d 21; 201.”
Construction and Comparison of High-Dimensional Sobol' Generators (2011, methodology): “Recurrent relationships for calculation of v i,j,1 are given in Joe and Kuo (2003). We derive a generalized variant of these relationships for an arbitrary k.”
Simulation and optimization approaches to scenario tree generation (2004, methodology): “One way to combat this is to use, instead of pseudorandom numbers, low-discrepancy Sobol sequences, Sobol (1967), and Bratley and Fox (1998).”
Solving Probabilistic Optimal Power Flow Problem Using Quasi Monte Carlo Method and Ninth-Order Polynomial Normal Transformation (2014, methodology): “A thorough introduction of the Sobol sequence is presented in [17] and [18].”
Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems (2011, unknown): “We make comparison with QMC, in which the complete system (16) is solved at 25, 000 Sobol points [29].”
Fast planning of well conditioned trajectories for model learning (2014, background): “More details of the implementation can be found in [10].”
Constructing Sobol Sequences with Better Two-Dimensional Projections (2008, methodology): “Some 2D projections of 4096 Sobol ′ points from [9].”
Design of computer experiments: A review (2017, methodology): “not discuss the sequence generation here, however, reader can refer to [18, 86] for understanding algorithm implementation.”
A unified deep artificial neural network approach to partial differential equations in complex geometries (2017, background): “A common choice is the Sobol sequence [34] which is described in detail in [2] for N ≤ 40, and later extended in [14] and [15] for N ≤ 1111, and N ≤ 21201, respectively.”
Ancient numerical daemons of conceptual hydrological modeling: 2. Impact of time stepping schemes on model analysis and prediction (2010, methodology): “[27] The total global sensitivity indices Sj TOT, based on the RMSE model performance measure, were calculated using 10,000 parameter sets sampled using quasi‐random Sobol’ sequences [Bratley and Fox, 1988].”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, background): “Direction numbers for s > 50 that also satisfy certain equidistribution properties can be found in [189, 262].”
Fast construction of good lattice rules (2007, methodology): “Finally the quasi-Monte Carlo rule uses low-discrepancy points (here Sobol’ points with direction numbers from [54]) to sample more uniformly and also has 64 samples per dimension.”